Thermal and Dynamics Analysis of Meniscus-Controlled Materials Processing

Fundamental physical processes involved in meniscus-controlled materials processing include meniscus formation and dynamics, movement of solidification interface, and the interaction at the crystal-liquid-vapor tri-junction. Final product shape that can be grown by different techniques depends on the meniscus shape, heat transfer and solidification interface. The fluid flow and heat transfer in the melt and dynamics of meniscus are critical for determining the stable growth conditions for better quality of the grown crystals. In this paper, a theoretical thermal and dynamic model have been developed to describe the heat transfer and dynamics of meniscus and its interaction with solidification. A simplified form of the model will also be developed to allow the investigation of ribbon (or tube) growth that exhibits one-dimensional feature in the most regions. This model will be used to conduct parametric study, and the important process and geometry conditions will be investigated such as the crystal dimension, die-top height, pull rate, and die-top temperature. The dynamic response of meniscus to the potential perturbations during growth such as pull rate and die-top temperature variations, and misalignment between the die and silicon tube will be investigated extensively. From this study, an operating window for stable meniscus will be obtained, and growth procedure that leads to improving the grown crystal quality will be identified.